A step that has a height of 6 inches. A ramp starts 5 feet away from the base of the step,making a 5.7 angle with ground. what can you say about the angle the ramp would make with the ground if the starts closer to the step?

The equation of ellipse with foci (-6,-1) and (-6,-7), and co-vertices (-2,-4) and (-10,-4) is [tex]\frac{(x+6)^2}{25}+\frac{(y+4)^2}{16}=1[/tex]

What is equation of an ellipse?

The standard equation of an ellipse centered at (h, k) with a major axis parallel to the x-axis is given by:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

where the coordinates of the vertex are (h±a, 0), coordinates of co-vertex are (h, k ± b) and the coordinates of foci are (h±c, k), where a² = c² + b².

According to the given question:

Given foci of the ellipse :

(-6, -1) and (-6, -7)

Co-vertices of the ellipse :

(-2, -4) and (-10, -4)

From the given foci and vertices ,

c = -1 - (-7) /2 = 3

b = -2 - (-10) /2 = 4

c² = a² + b²

∴ a² = 3 x 3 + 4 x 4 = 25

( h, k) = (-6 - 6 /2 , -1 - 7 / 2) = (-6, -4)

Equation of the ellipse is given by:

(x - h)²/ a² + (y - k)²/b² =1

(x - (-6))²/ 25 + (y - (-4))²/16 = 1

[tex]\frac{(x+6)^2}{25}+\frac{(y+4)^2}{16}=1[/tex]

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Answer: log81 = 1/4

Step-by-step explanation:

Log81^3

81^x = 3

The common base is 3, so

(3^4)^x=3

3^4x = 3^1

4x = 1

x= 1/4

Answer:

Step-by-step explanation:

o.67891

The minimum score Sam needs to get on his final exam to get a "C" in the course is 82.

What is a probability?

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

Given that, Sam's test scores are 62, 71, and 65.

The total score in three test is (62 + 71 + 65) = 198

Assume that, he scored x in the final test.

Total score of Sam is 198 + x.

He needs to score 70% means he needs to score 70 out of 100.

According to question,

(198 + x)/ 400 ≥ 70/100

Multiply both sides by 100:

(198 + x)/ 4 ≥ 70

Multiply both sides by 4

198 + x ≥ 280

x ≥ 280 - 198

x ≥ 82

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Answer:

y = 0

Step-by-step explanation:

x + 2y = 2 ( subtract 2y from both sides )

x = 2 - 2y → (1)

x = - 4y + 2 → (2)

substitute x = 2 - 2y into (2)

2 - 2y = - 4y + 2 ( add 4y to both sides )

2 + 2y = 2 ( subtract 2 from both sides )

2y = 0 , then

y = 0

Answer:

43 p

Step-by-step explanation:

total cost = 10 - 4.84 = 10.00 - 4.84 = £5.16

b + t = 5.16

t = 11b

b + 11b = 5.16

12b = 5.16

12 / 12 b = 5.16/12

b = £0.43

Answer: z > 14

Step-by-step explanation:

Move 3 to the right

Answer:

I think it's 0.5%

Step-by-step explanation:

16/32 x 100% = 0.5%

As the given polynomial -8y has only 1 term in is and hence it is classified as a monomial.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

x² 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The quantity of terms allows for the classification (naming) of polynomials.

A polynomial may contain exponents, constants, and variables, but it never divides by a variable.

They may also contain one or more terms, but not an infinite quantity.

The degree can also be used to categorize polynomials (the largest exponent of the variable).

An expression with only one term is called a monomial.

The sole term in an expression needs to be non-zero in order for it to be a monomial.

Therefore, as the given polynomial -8y has only 1 term in is and hence it is classified as a monomial.

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The value of the tangent of angle 37° is 3/4. Then the height of the cell tower will be 24.5 meters.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

A specialist gazes toward the highest point of a cell tower. The specialist stands 30 meters from the focal point of the pinnacle with a view of 37° from the level. The designer's eyes are 2 meters over the ground.

Let 'h' be the height of the tower. Then we have

tan 37° = (h - 2) / 30

Simplify the equation, then we have

tan 37° = (h - 2) / 30

3/4 = (h - 2) / 30

4h - 8 = 90

4h = 98

h = 24.5 meters

The level of the cell pinnacle will be 24.5 meters.

The diagram is given below.

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To perform a hypothesis test we use students' t distribution.

What is a hypothesis test?

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.

Here, we have

Given, the population mean is 13. the sample mean is 12.8, and the sample standard deviation is two. the sample size is 20.

We have to find distribution to perform a hypothesis test.

The students t distribution is used when

1- sample size less than 30. Here 20.

2-population standard deviation not given.

3-population is normal.

Hence, we concluded that to perform a hypothesis test we use students' t distribution.

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Answer:

5.75

Step-by-step explanation:

So first you would multiply 2.5*4.6 which is 11.5

Next you would divide 11.5/2 because a triangle is half of a square.11.5/2 is 5.75

For the given similar triangle the value of x will be 9 inches.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Since the two triangles are similar,

Suppose the unknown side is x,

Since the ratio of the sides of the similar triangles is equal the obtained expression is,

8/6=12/x

x=12×6 / 8

x=9 inches

Thus, for the given similar triangle the value of x will be 9 inches.

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Answer:

parallel

Step-by-step explanation:

same slope

Option 1 : x < = - 8 represents the given graph of inequality.

In mathematics, an inequality displays the connection between two values in an unbalanced algebraic expression. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signs.

Depending on which way the inequality sign is pointing, a sign can be greater or less than. When the open portion of the sign is facing left, >, the value on the left side of the sign is greater than the value on the right. When it is turned to the right, the left value is less than the right value.

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By solving an inequality, we will see that option a is cheaper for more than 60 miles.

We know that option A charges $25 per day plus $0.15 per mile, so the cost for x miles is given by the linear equation:

A(x) = $25 + $0.15*x

While for option B the fixed cost is $10 and the cost per mile is $0.40, so the cost equation is:

B(x) = $10 + $0.40*x

The cost of option a will be smaller when:

$25 + $0.15*x < $10 + $0.40*x

$25 - $10 < $0.40*x - $0.15*x

$15 < $0.25*x

$15/$0.25 < x

60 < x

So for 60 miles the cost is the same, for x > 60 miles the cost of option a will be smaller (because the slope is smaller).

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The equation of line through the origin and (-5, 6 ) is y = [tex]-\frac{6}{5}x[/tex]

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

the coordinates of the origin is (0, 0) and h other coordinates are (-5, 6)

at x = 0 and y = 0

using the equation of straight line y = mx + c

0 = 0(m) + c

so c = 0

at x = -5, y = 6

6 = -5m +c

but c = 0

6 = -5m

m = -6/5

Equation of line becomes y = -6/5x

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Answer:

A. [tex]y=11x[/tex]

Step-by-step explanation:

The graph is linear, meaning it follows the formula [tex]y=mx+b[/tex], where y and x are variables, m is the constant rate that the graph increases by, and b is the y-intercept. The graph is increasing at a rate of 55 calories burned per 5 minutes spent skateboarding, which simplifies to 11 calories per 1 minute, so m is 11. The graph's y-intercept is 0 because it runs through the origin, and there's no point in writing "11x + 0" so it's just "y = 11x"

Based on the definition of an equilateral triangle, the measure of angle KML is: d 60.

An equilateral triangle can be described as a triangle that has three sides that are equal and also equal interior angles that measures 60 degrees each.

The image shows that the three sides of triangle KML are marked equally by three strokes. This shows that the three sides of triangle KML are congruent to each other. Since they are congruent, they have equal length.

Therefore, triangle KML is an equilateral triangle that has interior angles that measures 60 degrees.

Angle KML is an interior angle of the equilateral triangle, therefore:

The measure of angle KML is: d. 60 degrees.

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Therefore, coin is unfair ,It is true that the coin can be considered unfair.

Calculating or estimating how likely or "possible" something is to occur is the subject of probability. Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring. Probabilities in mathematics are always expressed as fractions, decimals, or percent with values ranging from 0 to 1.

Here,

Step 1: We see that a coin is tossed 100 times, but we only receive heads 27 times.

In other words, the odds of a head are 27/100 or 0.27.

It is thought that there will be an equal number of heads and tails on a fair coin (or very close, if not equal).

So, using a fair coin:

P(H)=P(T)=0.5

Step 2

But in this instance, P(H)=0.27, which is a long way from 0.5.

Therefore, coin is unfair.

It is true that the coin can be considered unfair.

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With the help of congruency of triangles rules, we know that TSR ≅ QRS because of (B) the AAS congruence theorem.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

These triangles can be moved, turned, flipped, and rotated to produce the same appearance.

When moved, they are parallel to one another.

So, we have two sets of angles and one common side.

Review the congruence situations.

SSS ⇒ Three sides in the first, three sides in the second.

SAS: two sides, including the angle of the first side.

Incorporating angle in the second.

2 angles and the side that joins them in the first, according to ASA

Two angles and the side that connects the two angles.

AAS = 2 angles in the first triangle, plus 1 side.

Second, and one side in △.

Let's read the statements again and fill in the blanks.

Step 1: Since all right angles are congruent, mTSR = mQRS = 90°.

Step 2: Since it is given, mT = mQ

Step 3: Due to the reflexive property, SR becomes RS (common side)

Step 4: Because of the AAS congruence theorem, TSR and QRS are required.

Therefore, with the help of congruency of triangles rules, we know that TSR ≅ QRS because of (B) the AAS congruence theorem.

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The correct form of a question:
Given: TSR and QRS are right angles; T ≅ Q

Prove: TSR ≅ QRS

Step 1: We know that TSR ≅ QRS because all right angles are congruent.

Step 2: We know that T ≅ Q because it is given.

Step 3: We know that SR ≅ RS is because of the reflexive property.

Step 4: TSR ≅ QRS because __________

a. of the ASA congruence theorem

b. of the AAS congruence theorem

c. of the third angel theorem

d. all right triangles are congruent

Answer:

1. D 2. C 3. C

Step-by-step explanation:

On my test

Answer:

13

Step-by-step explanation:

You take the number of miles from weeks 5-8 and add them up. 2+3+4+4=13

Equation used to represent the relation between the number of pages written to the number of hours used with constant of proportionality is

x = 4y.

As given in the question,

Let us consider number of pages write by Bill be 'x'

And number of hours represented by 'y'

Number of hours used by Bill to write 4 pages = 1 hour

Number of pages written by Bill in 1 hour = 4

Given :

Number of pages is proportional to the number of hours

⇒ x ∝ y

⇒ x = ky

Where 'k' is the constant of proportionality.

When x = 4 , y = 1

substitute the value in the equation,

4 = k(1)

⇒ k = 4

Now the required equation with the constant of proportionality k = 4 is:

x = 4y

Therefore, the required equation to represent the relation between number of pages written to the number of hours used with constant of proportionality is equal to x =4y.

The complete question is:

Bill enjoys writing in his spare time. He writes 4 pages per hour. The proportional relationship between the number of pages written to the number of hours is represented by the equation ______. Write the equation in standard form with a constant of proportionality.

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The slope of the line passing through the points  (-9, 6) and (-3, 9) is (1/2).

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is

y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

We know slope(m) = (y₂ - y₁)/(x₂ - x₁).

Given, A line passes through the points (-9, 6) and (-3, 9).

∴ Slope(m) of the line is = (9 - 6)/(- 3 + 9) = 3/6 = 1/2.

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The number of animals will the farmer have after 7 months including the 10 cattle are 1280.

For the stated question-

Thus, number of animals after years;

= 10 x  2⁷

= 1280

Thus, number of animals will the farmer have after 7 months including the 10 cattle are 1280.

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For this we have to calculate 50% of 7,000 which is 3,500

What does a math percent mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula for percentage?

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

first we have to calculate 70% of 10,000 which is 7,000

Then now we have to calculate 50% of 7,000 which is 3,500

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